Seventh grade students plan graduation each year for the eighth graders. This year, they considered what would happen if we had to rent the chairs from a party company. Students researched online and made phone calls to determine pricing, and then wrote equations and created graphs to determine which company had the best prices based on renting anywhere from 0 to 500 chairs. Students prepared a report to submit their recommendations based on their findings. Click to see each student’s report.
We’ve been spending the past couple weeks understanding fractions and fraction operations. Students in fifth grade have been making some excellent hypotheses and asking wonderful questions about fractions. Here are some of the things they’re saying…
-2/3 x 3/5 = 6/15. I found this answer by finding 3/5 of 1 whole. The answer is 3/5. Then 3/5 became the whole. In other words, I am not finding 2/3 of a whole and 3/5 of a whole but finding 2/3 of 3/5. So I drew a picture to help me solve. I split a rectangle into fifths and shaded in 3 of them. I then covered that with 2/3 as 3/5 is my new whole. Then I shaded in 2 of the 3. This was 2/3 of 3/5. The answer was 6/15.
-2/3 x 3/5 was a very difficult problem but we figured it out. We got 2/5. It was 6/15 simplified into 2/5. It’s like you’re adding 2/3 3/5 of a time so it (the answer) would be smaller. 2/5 is smaller than 2/3 and 3/5.
-2/3 x 3/5 is a problem multiplying a fraction by a fraction. You will get a fraction of the original fraction. The product gets smaller.
-If you have a sheet of paper and you divide it into 5 sections you get 5ths. If you shade 3 sections in you get 3/5. You need 2/3 of that 3/5 so you take the 3/5 and split that into 3rds. Next you have to shade 2 of the 3rds you made. Now you have 6 boxes shaded. They are 15ths. Now you have 6/15 = 2/5 so 2/5 = 2/3 of 3/5.
-I noticed that the three in 2/3 times the 5 in 3/5 is 15 and the 2 in 2/3 times the 3 in 3/5 is 6. In total 6/15. Will this always occur when multiplying fractions?
-Will the way we did 2/3 x 3/5 work for every question like it?
Middle school students each shared two interesting facts about pi today to celebrate 3/14. A couple students referenced an old Star Trek episode where Spock used pi to outsmart an evil super computer. Math is everywhere!!
Fifth grade students used their knowledge of angles to construct ramps for snails to climb up while carrying their own weight. Students timed the snails and then recorded and graphed their distances. They determined the steeper the slope (larger the angle) the more challenging it was for the snails to climb up the ramp.
Sixth and seventh grade students participated in the Snail Olympics. They selected snails which competed in 4 events: sprinting, hurdles, tunneling, and mountain climbing. Students recorded the snails times and were awarded points based on what their snail accomplished. Students then determined unit rates and made different proportions using the data collected from the snails.
Alec gets to know his snail.
Whitley, Katrina, and Vivi measure how far their snail has gone.
Whitley uses a protractor to place the ramp at the correct angle.
Michael watches intently as his snail tunnels like a pro.
Allie is keeping an eye on her snail.
Joey, Ethan and Raphael giving their snail a pep talk before hurdles.
Chameli and Emily encourage their snail to go through the tunnel.
Alex’s snail tunneling along.
Marcello helps his snail through the tunnel.
Michael and Annika keeping an eye on their snail.
Students measure how far their snail has gone.
Students measure how far the snail has traveled.
John’s snail sneaks under the table during the sprint.
Chloe’s snail makes the hurdle over her pencil.
Michael helps his snail over the hurdle.
Sammy watches his snail climb a mountain.
Alek and Sydney cheer on their snail.
Special thanks to the Nazimov-Davis and Chehab families for volunteering to give the snails a happy home for their retirement!
Pre-Algebra students recently set a challenge for themselves. We have been working on solving larger equations and the students decided they would like to try to write their own story problems. We worked on solving these in class and thought it might be a good challenge for the Algebra I class to write and solve the equations as well. I look forward to seeing the equations and solutions!!
1) Steve and Joe both spend the same amount of money at the store. Joe buys $64 worth of soda for a party. He then realizes that he only needs half of that and gets rid of 1/2 of the soda. He buys the soda and then gives a donation. Steve buys $16 worth of groceries and gives a donation that is 3 times bigger than Joe’s. How big is Joe’s donation? (By: Chameli)
2) Jill and Tom work at a lemonade stand. Jill sells $x of lemonade and got a $1 tip each day. Tom sold $x of lemonade and got a $3 tip each day. Jill worked for 6 days and Tom worked for 4 days. They both made the same amount of money. How much money did they make each day? (By: Alex)
3) Enrique is running a marathon. He runs at a rate of 5 mph. Jesus shows up late to the marathon and is 10 minutes behind Enrique. Jesus runs at a rate of 8 mph. How long will it take for Jesus to catch up to Enrique? (By: Matt)
4) Billy Bob Joe bought a puzzle. It had 6 times more pieces than the last puzzle, 2 times more pieces than the one before that, 8 times more than the one before THAT, and 100 times more than the one before that. The earliest puzzle had four pieces. How many pieces is the puzzle that he is working on now? (By: Joey)
5) Millie the Silly has 4 dog bones for each dog. Big Max has 2 bones for each dog plus 4 extra bones. Millie and Max both have an equal amount of bones. How many dogs does each person have? (By: Marcello)
Recently, 7th grade students were tasked with the challenge of finding the height of a lamp post at the park. We had just begun exploring the idea of similar triangles and had been working on proportions earlier in the week. Students were not given any instruction on how to measure the lamp post, only that we weren’t estimating and that Matt knew he was 63 inches. They did notice how dramatic their shadows looked on the way to the park which helped them make the connection that they could find similar triangles. Check it out!
Video 1: Students measure Matt to make sure he is 63 inches.
Video 2: Students measure Matt’s shadow.
Video 3: Students finish measuring the lamp post shadow.
Video 4: Back in the classroom, students draw a picture to represent what they did, come up with the proportion equation, and talk about how to solve.
Video 5: Eureka!! Students determine the lamp post is 511″ or about 42 1/2′
Please make sure you are visiting The Hock’s Nest (password required). It is being updated regularly with what is happening in math class!! I’ve also suggested some things to ask your students about when they tell you their day was “fine” and they did “nothing” at school.
Oh my gosh, Johnny, look at that sign.
It is so backwards.
I mean, it looks like one of those signs
That didn’t get flipped.
I mean, who understands those inequality signs anyway?
I like inequalities and I can not lie
You mathletes can’t deny
When a number walks in with a negative sign
And you have to divide
You get FLIPPED!
And I pull out paper
I notice you want to start?
Deep in the equation I’m solving
I’m hooked and I can’t stop flipping
Oh Baby, I wanna flip ya.
The negative sign don’t miss ya
My homeboys tried to warn me
To flip that inequality
To multiply, or divide (divide!)
Both sides by a negative sign (sign!)
To keep everything true (true!)
Now you know what you gotta do
By “so far” I mean so far this year but more importantly…I can’t believe these kids have come so far!! This year’s class of Algebra I students have thoroughly impressed me with their engagement, interest, and problem solving prowess. I have been able to give the students a problem to solve, and sit back and listen with amazement as they discuss, justify, argue (mathematically), and grapple with the ideas being presented in the problem. They work to truly understand what is happening and why, and they continuously question each other and themselves in doing so. I feel so proud that these students, who I have watched grow since 5th grade, are so engaged in developing their own understanding.
For example, I recently gave them a problem involving vertical angles, with the angles labeled something like (2x + 9) degrees and (4x-3) degrees. I said their hint was that the angles were vertical and asked them to find x. They got right to work and not only looked up vertical angles when they didn’t remember the definition, but then determined they needed to set the two amounts equal to each other. They then proceeded to (correctly) solve for x, checking their work on their own to be sure. Additionally, I asked them to find the measure of the angles, which they happily did. (I’m not joking – I really think they were happy…I was ecstatic!) In the process, they were reviewing a property of vertical angles, and (the main goal of the lesson) solving an equation with a variable on both sides of the equal sign. I had not ever officially taught this concept to them before. Rather, they took what they knew about properties of equality and applied it to the problem. And guess what else…every student got this question correct on their chapter test and can explain what they are doing when solving. Keep up the great work Algebra I-ers.
